2009/3/27 Gael Guennebaud <gael.guennebaud@xxxxxxxxx>:
> On Fri, Mar 27, 2009 at 1:39 PM, Rohit Garg <rpg.314@xxxxxxxxx> wrote:
>>> hm, sorry that's not entirely true. I increased the number of samples,
>>> and for the fastest version:
>>>
>>> 1 iter = 42% of failures with max error = 2.78308e-07
>>> 2 iter = 36% of failures with max error = 2.15188e-07
>>> 3 iter = 34% of failures with max error = 1.87297e-07
>>
>> Failure? Do you mean that the error blows up for these values? But the
>> max error is pretty low. At any rate, the increased precision is too
>> low to iterate again compared to the perf hit, IMHO.
>
> don't panic, failure means error>0
OK, then indeed, the 2nd newton step is really not worth it. The
reason why it doesn't improve accuracy as much as theoretically, must
be that we are too close to the floating point numbers precision
already. Then, it seems to me that we can declare the precision to be
sufficient, as after the user will do a few operations on these
numbers, he will fall to a similar level of precision anyway.
Cheers,
Benoit